Abstract We extend the notion of Morita equivalence Poisson manifolds to setting formal structures, that is, power series bivector fields $\pi =\pi _0 + \lambda \pi _1 +\cdots $ satisfying integrability condition $[\pi ,\pi ]=0$. Our main result gives a complete description equivalent structures deforming zero structure ($\pi _0=0$) in terms $B$-field transformations, relying on general study d...

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including ordinary Hamiltonian G-spaces, Lu’s momentum maps of Poisson group actions, and the group-valued momentum maps of Alekseev–Malkin–Meinrenken. More precisely, we carry out the following program: (1) We de...

We introduce the notion of strong Morita equivalence for group actions on locally C-algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the locally C∗-algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes, Proc. London Math. Soc. 49(1984) and R. E. Curto, P....